Image data compression using multiple bases representation

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Abstract

The compression of gray scale images is an interesting problem because of the
large number of variations between data elements while maintaining a high degree of
correlation. The goal of image data compression is to obtain the best possible image for
a fixed information rate. In recent years, there has been a lot of research into the efficient
coding of gray scale images. Vector quantization (Va) methods have been successfully
applied to the efficient coding of images. These methods, however, are computationally
intensive. Full search Multiple Bases Representation (MBR) is similar to Va in many
respects. The Recursive Residual Projection (RRP) algorithm, a sub-optimal
implementation of full search MBR, has been found to perform well.

In this thesis, we apply MBR (using the RRP algorithm) to the compression of
image data. We develop an image coding system that allows for a comparison of MBR
with some well studied transform coding methods: the Discrete Cosine Transform (DeI)
and the Fast Haar Transform (FHT) coding methods. We find that the DCf based coder
performs at 1.5 bits/pixel with good image quality and that the FlIT based coder performs
at 0.81 bits/pixel with some disconcerting characteristics. The RRP based coder
outperforms the ncr based coder at 1.1 bits/pixel with very good image quality.

We also tested a modified version of the RRP algorithm that used 3 orthogonal
sets of basis vectors. We found that the modified RRP algorithm generally reduced the
number of representation coefficients and improved image quality. We also found that
the modified RRP algorithm performed worse than the RRP algorithm due to an increase
in symbol entropy.